That quest with monks was the first time when the game irritated me so much (not counting crashes of course). I have silently put all psychos to sleep but the monk yelled at me too. It was the moment when something broke inside me and I started killing with cold blood...I had this one cyberpsycho quest where I was asked to bring him in alive. I installed non-lethal mod on my weapon and took him down. After a while I looted the area and found an encrypted message that I accidentally closed instead of decrypting it. Couldn't find the message on my endless list of shards so I decided to reload a save and repeat the thing. This time I didn't bother to mod my weapon and I killed him dead, then decrypted the message. What happened was my fixer never mentioned anything about it when I returned the quest to her on both occasions. Later I read somewhere on the net that it doesn't seem to make a difference for that particular quest chain whether I take them alive or dead.
Another mission later on had this monk fellow that I was saving. The quest giver asked for no bloodshed and it was OK by me as I always favor non-lethal stealth takedowns. I used non-lethal takedown on all the enemies on the map and hid their bodies in safe places (not in containers as the area didn't have any) but upon saving the hostage I got yelled at for shedding blood.
Apparently that was another mission where non-lethal mattered none. Pretty sure you can't talk your way through that mission but there's a slight possibility I could have managed to distract the enemies to open a safe way to the hostage. Too bad I don't have a manual save from that part to check. Guess that's a thing for the later play through.
No, there was no way to safe that monk without fight. Quest was quite specific to eliminate all hostiles. If you tried to approach the maelstorm guarding a front door, he threatened you with a gun to go away.